Question

1. a square has a side length of (6 + 3x) feet. an equilateral triangle has a side length of (8x - 2) feet. the perimeter in feet of the square is equal to the perimeter in feet of the triangle. what is the value of x? x = 1.6 x = 2.5 x = 0.5 x = 0.4 clear all

Explanation:

Step1: Find perimeter of square

The perimeter of a square $P_{square}$ with side - length $s$ is $P_{square}=4s$. Here, $s = 6 + 3x$, so $P_{square}=4(6 + 3x)=24+12x$.

Step2: Find perimeter of equilateral triangle

The perimeter of an equilateral triangle $P_{triangle}$ with side - length $t$ is $P_{triangle}=3t$. Here, $t = 8x−2$, so $P_{triangle}=3(8x - 2)=24x-6$.

Step3: Set perimeters equal and solve for $x$

Since $P_{square}=P_{triangle}$, we have the equation $24 + 12x=24x-6$.
Subtract $12x$ from both sides: $24=24x-12x - 6$, which simplifies to $24 = 12x-6$.
Add 6 to both sides: $24 + 6=12x$, so $30 = 12x$.
Divide both sides by 12: $x=\frac{30}{12}=2.5$.

Answer:

$x = 2.5$